A Revisit to stability of schauder bases: Fractalizing multivariate faber-schauder system

Navascues, M. A. (Universidad de Zaragoza) ; Viswanathan, P.

Resumen: Let X be a Banach space with a Schauder basis (xm)m=08, and I be the identity operator on X. It is known, at least in essence, that if (Tm)m=08 is a sequence of bounded linear operators on X such that am=08aI-T ma < 8, then (Tm(xm))m=08 is also a basis. The first part of this work acts as an expository note to formally record the aforementioned stability result. In the second part, we apply this stability result to construct a Schauder basis consisting of bivariate fractal functions for the space of continuous functions defined on a rectangle. To this end, fractal perturbations of the elements in the classical bivariate Faber-Schauder system are formulated using a sequence of bounded linear fractal operators close to the identity operator in accordance with the stability result mentioned above. This illustration, although emphasized only for the bivariate case, can easily be extended to higher dimensions. Further, the perturbation technique used here acts as a companion for a few researches on fractal bases in the univariate setting. © 2022 World Scientific Publishing Company.

Idioma: Inglés

DOI: 10.1142/S0218348X2272001X

Año: 2022

Publicado en: Fractals 30, 3 (2022), 2272001 - 908
ISSN: 0218-348X

Factor impacto JCR: 4.7 (2022)

Categ. JCR: MATHEMATICS, INTERDISCIPLINARY APPLICATIONS rank: 11 / 107 = 0.103 (2022) - Q1 - T1
Categ. JCR: MULTIDISCIPLINARY SCIENCES rank: 21 / 73 = 0.288 (2022) - Q2 - T1

Factor impacto CITESCORE: 6.6 - Mathematics (Q1)

Factor impacto SCIMAGO: 0.6 - Multidisciplinary (Q1) - Modeling and Simulation (Q2) - Applied Mathematics (Q2) - Geometry and Topology (Q2)

Tipo y forma: Article (PostPrint)

Área (Departamento): Área Matemática Aplicada (Dpto. Matemática Aplicada)